Lab 7 Rotational Equilibrium - Torques

Transcription

1 Lab 7 Rotational Equilibrium - Torques Objective: < To test the hypothesis that a body in rotational equilibrium is subject to a net zero torque and to determine the typical tension force that the biceps must produce. Equipment: < Arm assembly < Table clamp, 60 cm rod, and a swivel clamp < Hooked weight set < Force sensor < Computer with Pasco interface and Science Workshop Physical Principles: A torque is produced about an origin when a force acts at a point of a body in a direction other than the direction of the origin from this point. Torques tend to make a body rotate about an axis. Those torques that rotate a body in a clockwise direction are called clockwise and are usually described by negative numbers. Those that rotate a body in a counterclockwise direction are called counterclockwise and are usually described by positive numbers. Figure 1 Torque about an origin generated by a force. The torque generated by a force F acting at a point which is a distance, d, from the origin is defined as = Fperp d (1) F perp is the component of the force perpendicular to the line from the origin to the point of action of the force and therefore is given by F perp = F sin 2. In figure 1 2 is the angle between this line and the direction of the force. The distance d is called the length of the lever arm. If a body is in rotational equilibrium the net torque acting on it must be zero. Figure 2 Generation of a counterclockwise torque. Procedure: Setup Science Workshop, and calibrate the force sensor as done in previous laboratories.

2 Lab 7 Rotational Equilibrium - Torques Objective: < To test the hypothesis that a body in rotational equilibrium is subject to a net zero torque and to determine the typical tension force that the biceps must produce. Equipment: < Arm assembly < Table clamp, 60 cm rod, and a swivel clamp < Hooked weight set < Force sensor < Computer with Pasco interface and Science Workshop Physical Principles: A torque is produced about an origin when a force acts at a point of a body in a direction other than the direction of the origin from this point. Torques tend to make a body rotate about an axis. Those torques that rotate a body in a clockwise direction are called clockwise and are usually described by negative numbers. Those that rotate a body in a counterclockwise direction are called counterclockwise and are usually described by positive numbers. Figure 1 Torque about an origin generated by a force. The torque generated by a force F acting at a point which is a distance, d, from the origin is defined as = Fperp d (1) F perp is the component of the force perpendicular to the line from the origin to the point of action of the force and therefore is given by F perp = F sin 2. In figure 1 2 is the angle between this line and the direction of the force. The distance d is called the length of the lever arm. If a body is in rotational equilibrium the net torque acting on it must be zero. Figure 2 Generation of a counterclockwise torque. Procedure: Setup Science Workshop, and calibrate the force sensor as done in previous laboratories.

3 Refer to figures 3 and 4 for the measurements in steps 1 and 2. Record the mass m arm and length l arm of the wooden forearm. Also calculate the weight m arm g of the wooden forearm. The length of the forearm lever arm l arm should be taken to be the length from the center of the joint screw to the center of the hole on the opposite end that contains the thread supporting the load. Record the distance d cg of the forearm center to the elbow joint and the distance d m of the attachment point to the joint. The distance of the forearm center to elbow d cg should be taken to be the length from the middle of the forearm to the center of the joint screw. The distance of muscle attachment d m should be from the center of the hole with the upper support string to the center of the joint screw. Setup 1 With the upper arm approximately vertical adjust its position in the clamp so that the lower arm is horizontal (see figure 3). You may wish to sight along the horizontal wall joints to level the forearm. Measure and record the angle 2, and record the tension from the scale. Then make the following calculations: Torque due to the Load = W load l arm Torque do to the Forearm = W arm d cg 2. Compute the counterclockwise torques: Torque due to support = T d m sin 2 3. Compare the total clockwise torque with the counterclockwise torque by computing the Figure 3 Diagram of Setup 1. percent error. This is done by dividing the difference of the two torques (clockwise and counterclockwise) by their average and multiplying by 100. Setup 2 Position the upper arm vertically and the lower arm at an angle of about 40E above the horizontal. Repeat the calculations of setup 1 noting that the clockwise torque calculations must include the additional factor of cos a where a is the angle of the forearm above the horizontal. Torque due to the Load = W load l arm cos a Torque do to the Forearm = W arm d cg cos a Figure 4 Diagram of Setup 2.

4 Refer to figures 3 and 4 for the measurements in steps 1 and 2. Record the mass m arm and length l arm of the wooden forearm. Also calculate the weight m arm g of the wooden forearm. The length of the forearm lever arm l arm should be taken to be the length from the center of the joint screw to the center of the hole on the opposite end that contains the thread supporting the load. Record the distance d cg of the forearm center to the elbow joint and the distance d m of the attachment point to the joint. The distance of the forearm center to elbow d cg should be taken to be the length from the middle of the forearm to the center of the joint screw. The distance of muscle attachment d m should be from the center of the hole with the upper support string to the center of the joint screw. Setup 1 With the upper arm approximately vertical adjust its position in the clamp so that the lower arm is horizontal (see figure 3). You may wish to sight along the horizontal wall joints to level the forearm. Measure and record the angle 2, and record the tension from the scale. Then make the following calculations: Torque due to the Load = W load l arm Torque do to the Forearm = W arm d cg 2. Compute the counterclockwise torques: Torque due to support = T d m sin 2 3. Compare the total clockwise torque with the counterclockwise torque by computing the Figure 3 Diagram of Setup 1. percent error. This is done by dividing the difference of the two torques (clockwise and counterclockwise) by their average and multiplying by 100. Setup 2 Position the upper arm vertically and the lower arm at an angle of about 40E above the horizontal. Repeat the calculations of setup 1 noting that the clockwise torque calculations must include the additional factor of cos a where a is the angle of the forearm above the horizontal. Torque due to the Load = W load l arm cos a Torque do to the Forearm = W arm d cg cos a Figure 4 Diagram of Setup 2.

5 2. Compute the counterclockwise torques: Torque due to support string = F FS d m sin 2 3. Compare the total clockwise torque with the counterclockwise torque by computing the percent error. This is done by dividing the difference of the two torques (clockwise and counterclockwise) by their average and multiplying by 100. Estimating the tension in a muscle Using the results from setups 1, 2, and 3, explain what positions of arm and forearm allow you to lift a weight in your hand most easily. Try this with a 1 kg mass. Estimate the muscle tension when you are raising a weight of about 20 N in your hand when the upper arm and forearm are nearly horizontal. Make reasonable estimates of the angles and lengths and neglect the weight of your forearm. Data and Results: m arm = m load = l arm = d m = d cg = Part 1 2 = Load torque = m load g l arm = Beam weight torque = m arm g d cg = F FS = Support string torque = J = F FS d m sin 2 = Part 2 2 = a = Load torque = m load g l arm cos a = Beam weight torque = m arm g d cg cos a = F FS = Support string torque = J = F FS d m sin 2 =

6 2. Compute the counterclockwise torques: Torque due to support string = F FS d m sin 2 3. Compare the total clockwise torque with the counterclockwise torque by computing the percent error. This is done by dividing the difference of the two torques (clockwise and counterclockwise) by their average and multiplying by 100. Estimating the tension in a muscle Using the results from setups 1, 2, and 3, explain what positions of arm and forearm allow you to lift a weight in your hand most easily. Try this with a 1 kg mass. Estimate the muscle tension when you are raising a weight of about 20 N in your hand when the upper arm and forearm are nearly horizontal. Make reasonable estimates of the angles and lengths and neglect the weight of your forearm. Data and Results: m arm = m load = l arm = d m = d cg = Part 1 2 = Load torque = m load g l arm = Beam weight torque = m arm g d cg = F FS = Support string torque = J = F FS d m sin 2 = Part 2 2 = a = Load torque = m load g l arm cos a = Beam weight torque = m arm g d cg cos a = F FS = Support string torque = J = F FS d m sin 2 =